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In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrained by a PDE of continuity-type, governing the dynamics of the probability distribution of the agent population. We show the existence of mean field optimal controls both in the stochastic and deterministic setting. We derive rigorously the first order optimality conditions useful for numerical computation of mean field optimal controls. We introduce a novel approximating hierarchy of sub-optimal controls based on a Boltzmann approach, whose computation requires a very moderate numerical complexity with respect to the one of the optimal control. We provide numerical experiments for models in opinion formation comparing the behavior of the control hierarchy. ; ERC advanced Grant 668998 (OCLOC) ; (VLID)2523620

AbstractThe power of the symbolic mathematics program Maple is demonstrated for teaching topics from microeconomics (the benefits of portfolio diversification) and econometrics (a geometric perspective of multicollinearity). In particular, it appears that the use of symbolic mathematics programs has excellent potential to strengthen the development and integration of graphical and algebraic intuition for a wide variety of economic problems.

It is important to monitor and assess the physiological strain of individuals working in hot environments to avoid heat illness and performance degradation. The body core temperature (Tc) is a reliable indicator of thermal work strain. However, measuring Tc is invasive and often inconvenient and impractical for real-time monitoring of workers in high heat strain environments. Seeking a better solution, the main aim of the present study was to investigate the Kalman filter method to enable the estimation of heat strain from non-invasive measurements (heart rate (HR) and chest skin temperature (ST)) obtained 'online' via wearable body sensors. In particular, we developed two Kalman filter models. First, an extended Kalman filter (EFK) was implemented in a cubic state space modelling framework (HR versus Tc) with a stage-wise, autoregressive exogenous model (incorporating HR and ST) as the time update model. Under the second model, the online Kalman filter (OFK) approach builds up the time update equation depending only on the initial value of Tc and the latest value of the exogenous variables. Both models were trained and validated using data from laboratory- and outfield-based heat strain profiling studies in which subjects performed a high intensity military foot march. While both the EKF and OKF models provided satisfactory estimates of Tc, the results showed an overall superior performance of the OKF model (overall root mean square error, RMSE = 0.31°C) compared to the EKF model (RMSE = 0.45°C).

The Government of Montenegro nationalized 2030 Agenda on Sustainable Development by adopting the National Strategy for Sustainable Development (NSSD) in 2016, together with a corresponding Action Plan for its implementation. The NSSD is umbrella, horizontal and long-term development strategy of Montenegro that relates not only to environment and economics, but also to human resources, valuable social capital that should ensure prosperous development, recommendations for establishing the framework of financing and governance for sustainable development. The NSSD represents strategic framework for the transposition of the UN sustainable development goals (SDGs) and its indicators into national context. The NSSD Action plan, divided into 6 thematic areas with 30 strategic goals of sustainable development of Montenegro and their 102 measures and 601 sub-measures, represents very complex mechanism for monitoring and reporting about achieving the UN sustainable development goals (SDGs) in Montenegro. Hence, measuring progress in the NSSD implementation is the focus of this research. Effective measuring of the progress in the NSSD implementation could be achieved under the following preconditions: developed coordination mechanism for reporting, methodology of designing indicators, IT support for data collection and reporting, and strengthening of inter-linkages between the EU agenda and UN 2030 Agenda.

Genetic diversity of crop plants is being further explored and exploited to generate higher crop yield, better disease resistance, and more nutritional value. This book focuses on using genetic resources to mitigate the effects of climate change and increase crop production. It emphasises recent advances in mathematics and omics technologies addressing issues related to adaptation of crops to changing climatic conditions.--

3.3 The Bond's Yield, Duration, Modified Duration, and Convexity3.4 Risk Management; Reference; Section II Theory; Chapter 4 The Term Structure of Interest Rates; 4.1 The Economy; 4.2 The Traded Securities; 4.3 Interest Rates; 4.4 Forward Prices; 4.5 Futures Prices; 4.6 Option Contracts; 4.6.1 Definitions; 4.6.2 Payoff Diagrams; 4.7 Summary; References; Chapter 5 The Evolution of the Term Structure of Interest Rates; 5.1 Motivation; 5.2 The One-Factor Economy; 5.2.1 The State Space Process; 5.2.2 The Bond Price Process; 5.2.3 The Forward Rate Process; 5.2.4 The Spot Rate Process